Integers are the whole numbers and their negatives — like −3, 0, and 7. Once you can picture them on a number line, adding and subtracting them (even the negative ones) becomes a set of simple, reliable moves.
Integers are whole numbers, their opposites, and zero. There are no fractions or decimals. On a number line, positive numbers sit to the right of zero and negative numbers sit to the left.
A temperature of −5° is 5 degrees below zero. An elevation of −200 ft is below sea level. Owing a friend $3 is like having −3 dollars.
To add, start at the first number, then move: right for a positive number, left for a negative one. Where you land is your answer.
Once you get the idea, you don't need to draw every time. Look at the two signs:
Add the two amounts and keep that shared sign.
Subtract the smaller amount from the larger, and keep the sign of the larger one.
Positives pull right, negatives pull left. If the two sides are equal, they cancel to zero. Otherwise the stronger side wins by the difference between them.
Here's the one trick that makes subtraction easy — Keep, Change, Change. Keep the first number, change the minus to a plus, and change the second number to its opposite. Then just add.
Leave the first number alone.
Change subtraction into addition.
Flip the sign of the second number to its opposite.
Two negatives next to each other turn into a positive: subtracting −7 is the same as adding 7. "Minus a minus" means "plus."
Solve each one, then check. Stuck? Use the hint, or reveal the number line to see the moves.